Question

Determine the x intercepts, y intercept, equation of the axis of symmetry and vertex for each of the following functions,
1.) f(x)= 3(x-2)^2-6 with zeros of 0.59 and 3.41
2.) g(x)= (x-4)(x+7)

Answer 1

1. f(x)= 3(x-2)^2-6 with zeros of 0.59 and 3.41

everything you asked for , except the y-intercept, can simply be stated directly from the equation:
x-intercepts, you stated them already
axis of symmetry: x-2 = 0 or x = 2
vertex: (2,-6)

for the y-intercept, let x = 0
y = 3(-2)^2 - 6 = 6

g(x) = (x-4)(x+7)
x intercepts: x = 4 and x = -7
the vertex is half-way between 4 and -7
so the x of the vertex is (-7+4)/2 = -3/2
sub that in ...
y = (-3/2 - 4)(-3/2 + 7) = -121/4
vertex is (-3/2 , -121/4)
axis of symmetry : x = -3/2
yintercept: let x = 0
y = (-4)(7) = -28